There are an infinite variety of concepts. You can define the concept of a hand to start at the end of the large arm bones, or merely at the first of the hand bones. Describing the edge cases to a commonly used concept does not invalidate it outside the range of those edge cases. Colors exist although they have fuzzy, gradient boundaries between other colors.
The western concepts of man and woman exist no less, describe the world no less than they ever have- even if culture moves on from them. We could call women "biological females" and men "biological males" and all that has changed is how the concepts are linked to syllables. Culture does not dictate what can be recognized. The universe allows all possible categorizations, all possible discrimination. There is a logical relationship between every person to comprehend a concept and every thing that they would be able to validate against that definition. Every man throughout history who has ever considered some variation of the "biological female" commonly known as "woman" concept has implicitly recognized the distinction between all so called "trans women" and women. There are estimates that roughly 117 billion humans have existed on earth. Nearly 12 billion people ten times over, easily a billion people a hundred times over recognized for their entire lives the distinction between what you are and what you want to be. The concepts in their heads are looking at you. It is strange how cultures attune people to understand what is existentially important, what is lethal. In the west there is an obsession with image, with how you are perceived. In Africa there are witch doctors who can stop a man's heart with nothing but his fear, his belief in the power of the curse.
[another paragraph about natural categories- the root of a tree vs the dirt around it. Something to help automatically rank the value of categories, contrasting slightly with the intro subjectivity]